RBF Surrogate Global Optimization Algorithms and Intelligent Memory Management to Reduce HPC Parallel Computational Effort for Hydrological Models with an Application to Lake Hydrodynamics PDE Model

Abstract:

This paper discusses optimization algorithms and memory management that can significantly improve model parameter calibration and management analysis for a wide range of hydrological and other geophysical problems described by expensive simulation models, including nonlinear, coupled transient partial differential equations (PDE). Since transient PDE models are expensive to compute over the simulation period, we also developed an efficient parallel optimization algorithm to reduce wallclock time. The algorithm also runs efficiently in serial.

The proposed optimization and memory methods are demonstrated on calibration of model parameters for a three-dimensional spatial and temporal PDE description of hydrodynamics and water quality (including multiple species of nitrogen and phosphorous as well as algae) in a lake of over 230 hectares

Importantly, there is no assumption that model parameters have a linear or convex impact on functions that compute model error. Hence this is a global optimization method for a black box problem to find the best model parameters. The algorithm has theoretically based convergence properties and is very efficient numerically. The algorithm is general purpose: it can be used on other kinds of models including those PDE models (e.g. groundwater contaminant fate and transport models) with outputs that are not linear or convex functions of their parameters.

The algorithm is well suited for parameter calibration of expensive simulation models for which relatively few evaluations can be made because the algorithm utilizes a radial basis function (RBF) as a surrogate approximation of objective function that helps efficiently guide the optimization search. The optimization algorithm can also deal with asynchronous parallelism and/or high- dimensional problems that arise when a large number of model parameters are being considered simultaneously.

Also demonstrated is the impact of computer memory issues when doing simulations of complex PDE models on separate computer cores simultaneously (i.e. parallel processing) on a node. The analysis shows that when solving many PDE models at once in parallel, memory issues can cause significant runtime slowdown and longer runtime for each simulation. An effective method is implemented that adjusts the memory management during the computation to mitigate this problem.

Optimization code and an optional interface for Delft 3D open source water software available from authors.